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Rotationally driven ‘zebra stripes’ in Earth’s inner radiation belt


Structured features on top of nominally smooth distributions of radiation-belt particles at Earth have been previously associated with particle acceleration and transport mechanisms powered exclusively by enhanced solar-wind activity1,2,3,4. Although planetary rotation is considered to be important for particle acceleration at Jupiter and Saturn5,6,7,8,9, the electric field produced in the inner magnetosphere by Earth’s rotation can change the velocity of trapped particles by only about 1–2 kilometres per second, so rotation has been thought inconsequential for radiation-belt electrons with velocities of about 100,000 kilometres per second. Here we report that the distributions of energetic electrons across the entire spatial extent of Earth’s inner radiation belt are organized in regular, highly structured and unexpected ‘zebra stripes’, even when the solar-wind activity is low. Modelling reveals that the patterns are produced by Earth’s rotation. Radiation-belt electrons are trapped in Earth’s dipole-like magnetic field, where they undergo slow longitudinal drift motion around the planet because of the gradient and curvature of the magnetic field. Earth’s rotation induces global diurnal variations of magnetic and electric fields that resonantly interact with electrons whose drift period is close to 24 hours, modifying electron fluxes over a broad energy range into regular patterns composed of multiple stripes extending over the entire span of the inner radiation belt.

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Figure 1: Zebra stripe patterns in energetic electron distributions from the inner radiation belt.
Figure 2: Global diurnal oscillations of the electric and magnetic fields produced by Earth’s rotation.
Figure 3: Formation of zebra stripes.


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This work was supported by NSF grant AGS1059736, NASA grant NNX11AO74G and NASA contract NAS5-01072 through a subcontract from NJIT 999640-I. We thank A. Marcotte (JHU/APL) for help with Fig. 2.

Author information




A.Y.U. was lead author, developed the hypothesis of the rotationally driven nature of the zebra pattern and was responsible for all theoretical analysis. M.I.S. contributed to theoretical analysis and simulations. D.G.M. was responsible for the RBSPICE data analysis. K.T. provided consultations on the ULF wave–particle interaction. L.J.L. and B.H.M. participated in data analysis and in the interpretation of theoretical work.

Corresponding author

Correspondence to A. Y. Ukhorskiy.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 A zebra stripe pattern from the RBSPICE A perigee pass on 30 March 2013.

Differential intensity (shown with colour) of energetic electrons as function of time along a perigee pass through the inner radiation belt (radial distance L in Earth radii is marked on the top). Bottom panel, the energy dependence (in keV) of differential intensity for electrons with approximately 90o pitch angles. Upper panel, the pitch-angle distribution of the intensity of 230 keV electrons. It shows highly pronounced stripes that are curved towards more field-aligned particles. The ringed numbers plotted along the 230 keV line in the bottom panel and along the 90o values in the upper panel show the correspondence of stripes in the energy and pitch-angle spectra.

Extended Data Figure 2 Formation of zebra stripes in the process of stretching and folding of the electron phase space density distribution.

a, c, Smooth initial phase space density independent of the drift angle f(K) (a); points A, B and C with different drift angle (θ) values but the same energy K (radial position) correspond to the same value of the phase space density (c). b, d, The moment in the stretching and folding process when points A, B and C are aligned along the azimuthal angle where a spacecraft observation is taken (d). Points A, B and C are separated in energy at the same level of the phase space density, which requires formation of a local peak in phase space density (b) corresponding to a stripe of the emerging zebra pattern.

Extended Data Figure 3 Long-term evolution of a zebra pattern under steady-state conditions.

Four panels show electron intensity (j = p2f) as function of energy along the surface of a constant adiabatic invariant (same as Fig. 3 and Supplementary Video 2) at different moments (top to bottom, time T = 1, 2, 3 and 4 days) of a long-term simulation of electron motion in the presence of global diurnal oscillations in the electric field. Stretching and folding leads to a continuous increase of the number of stripes associated with the decrease in their width and spacing.

Supplementary information

Emergence of zebra patterns due to Earth’s rotation

Left panel: energetic electron distribution measured by RBSPICE during quiet geomagnetic conditions (also shown in Figure 1a). Right panel: evolution of an initially smooth electron distribution due to global diurnal oscillations in the inductive electric field (a snapshot shown in Figure 1d). (MP4 459 kb)

Phase space mixing leading to formation of zebra stripes

Phase-space evolution of an initially smooth distribution of electron phase space density due to global diurnal oscillations in the inductive electric field (a snapshot shown in Figure 3b). (MP4 5785 kb)

Effects of geomagnetic activity (Example 1)

Left panel: energetic electron distribution measured by RBSPICE during active geomagnetic conditions (also shown in Figure 1f). Right panel: evolution of an initially smooth electron distribution due to a combined effect of global diurnal oscillations and recurrent magnetospheric substorms with the period between 2 and 4 hours (a snapshot shown in Figure 1h). (MP4 300 kb)

Effects of geomagnetic activity (Example 2)

Left panel: energetic electron distribution measured by RBSPICE during active geomagnetic conditions (also shown in Figure 1e). Right panel: evolution of an initially smooth electron distribution due to a combined effect of global diurnal oscillations and recurrent magnetospheric substorms with the period (modified compared to Example 1) between 2 and 6 hours. (MP4 450 kb)

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Ukhorskiy, A., Sitnov, M., Mitchell, D. et al. Rotationally driven ‘zebra stripes’ in Earth’s inner radiation belt. Nature 507, 338–340 (2014).

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